Deck 12: Statistical Thermodynamics

Question 1

The monosaccharide ribose, C₅H₁₀O₅ may exist in five distinct conformations. Two of these conformations are six-membered rings and two are five-membered rings, with the remaining conformation being a straight chain. In a solution at 25 C, a sample of ribose was found to exist as 60% α-D-ribopyranose and 21% β-D-ribopyranose. Calculate the difference in molar energy between these two conformations, which differ only in the orientation of the anomeric hydroxyl group

A) 0.22 kJ mol^-1
B) 1.2 kJ mol^-1
C) 2.6 kJ mol^-1
D) 4.0 kJ mol^-1

Answer 1

C

Question 2

Calculate the translational partition function of a carbon dioxide, CO₂, molecule in a sample of 0.250 mol of gas held in a vessel at a pressure of 1.00 bar and a temperature of 298 K.

A) 0
B) 1.0
C) 2.3  10¹⁹
D) 1.8  10²⁹

Answer 2

D

Question 3

Calculate the rotational partition function for acetylene, C₂H₂, at 298 K. The rotational constant of acetylene is 3.529  10¹⁰ Hz.

A) 88
B) 1.0
C) 176
D) 53

Answer 3

A

Question 4

The harmonic vibrational wavenumber of an iodine, I₂, molecule is 217 cm^-1. Treating the molecule as a harmonic oscillator, calculate the vibrational partition function at 298 K.

A) 0.955
B) 1.00
C) 0
D) 1.523

Question 5

The vibrational modes of a methane molecule, CH₄, are listed below. Calculate the vibrational partition function at 1000 K.

A) 1.0
B) 2.04
C) 1.33
D) 17.2

Question 6

The degeneracy of the lowest level of a Br atom is 4. The first excited electronic level lies the equivalent of 3685 cm^-1 higher in energy and has a degeneracy of 2. Calculate the electronic partition function at a temperature of 2500 K.

A) 4.24
B) 1.00
C) 4.00
D) 6.00

Question 7

Calculate the contribution made by vibrational motion to the molar entropy of hydrogen iodide, HI, gas at a temperature of 500 K. The vibrational frequency of HI is 7.91  10¹² s^-1.

A) 8.31 J K^-1 mol^-1
B) 16.6 J K^-1 mol^-1
C) 10.6 J K^-1 mol^-1
D) 6.02 J K^-1 mol^-1

Question 8

Use statistical thermodynamics to derive an expression for the contribution to the molar heat capacity at constant volume of a diatomic molecule at a temperature of 298 K as a result of vibrational motion. Start by differentiating with respect to temperature the expression for the internal energy and substituting for the vibrational partition function.

A) C_V,m=3/2 R
B) C_V,m=5\/2 R
C)C_V,m= R
D) C_V,m=2 R

Question 9

Water, H₂O, has a residual entropy of 3.4 J K^-1 mol^-1 at 0 K, which arises because each water molecule may be orientated in two distinct ways. Use the Boltzmann formula to predict the residual entropy of mono-deuterated water, HDO.

A) 5.8 J K^-1 mol^-1
B) 9.2 J K^-1 mol^-1
C) 3.4 J K^-1 mol^-1
D) 0 J K^-1 mol^-1

Question 10

Calculate the standard molar Gibbs energy of argon gas, Ar, at a temperature of 298 K, relative to that at 0 K.

A) -31.4 kJ mol^-1
B) +2.48 kJ mol^-1
C) -148 kJ mol^-1
D) -59.9 kJ mol^-1